# Deep learning for full-field ultrasonic characterization

arXiv: https://arxiv.org/abs/2301.02378 · HTML: https://mlsanity.com/paper/2301.02378/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 6 Jan 2023.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Improved architectures and training algorithms for deep operator networks](https://mlsanity.com/paper/2110.01654/) (2021)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture](https://mlsanity.com/paper/2005.00615/) (2020)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements](https://mlsanity.com/paper/2204.00205/) (2022)

## Built on by (most cited first, 5 of 5)

- [Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements](https://mlsanity.com/paper/2409.20510/) (2024)
- [Network scaling and scale-driven loss balancing for intelligent poroelastography](https://mlsanity.com/paper/2411.08886/) (2024)
- [Channel Fingerprint Construction for Massive MIMO: A Deep Conditional Generative Approach](https://mlsanity.com/paper/2505.07893/) (2025)
- [Newton-Puiseux Analysis for Interpretability and Calibration of Complex-Valued Neural Networks](https://mlsanity.com/paper/2504.19176/) (2025)
- [Deep regularization networks for inverse problems with noisy operators](https://mlsanity.com/paper/2506.07008/) (2025)

## Abstract (arXiv)

This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two logics, namely the direct inversion and physics-informed neural networks (PINNs), are explored. The direct inversion entails three steps: (i) spectral denoising and differentiation of the full-field data, (ii) building appropriate neural maps to approximate the profile of unknown physical and regularization parameters on their respective domains, and (iii) simultaneous training of the neural networks by minimizing the Tikhonov-regularized PDE loss using data from (i). PINNs furnish efficient surrogate models of complex systems with predictive capabilities via multitask learning where the field variables are modeled by neural maps endowed with (scaler or distributed) auxiliary parameters such as physical unknowns and loss function weights. PINNs are then trained by minimizing a measure of data misfit subject to the underlying physical laws as constraints. In this study, to facilitate learning from ultrasonic data, the PINNs loss adopts (a) wavenumber-dependent Sobolev norms to compute the data misfit, and (b) non-adaptive weights in a specific scaling framework to naturally balance the loss objectives by leveraging the form of PDEs germane to elastic-wave propagation. Both paradigms are examined via synthetic and laboratory test data. In the latter case, the reconstructions are performed at multiple frequencies and the results are verified by a set of complementary experiments highlighting the importance of verification and validation in data-driven modeling.